# Why do waves disappear after some time?

When a stone is thrown in water then transverse waves are formed. But they get slow and disappear after sometime. Why?

Similarly it happens in longitudinal waves. When we speak, after sometime our voice gets faint.

In both cases there is a disturbance of short duration which moves outwards in all directions : the splash of the stone or the noise of a shout. The disturbance transfers a limited amount of energy into the medium (water or air). As the disturbance moves outwards the energy it carries is spread over a larger and larger region called the wave-front.

For example, the ripples in the water lie on a circle with an ever-increasing circumference. The amplitude of the ripples decreases as the circumference of the circle increases. Eventually the ripples are so faint that they cannot be distinguished from the ripples formed by much smaller random disturbances caused by puffs of wind, reflections from a river bank or from stones which break the surface, fish breaking the surface of the water, etc.

In the case of your voice the amplitude of the sound wave (which is a pressure wave) becomes as small as the random variations in the pressure of the air caused by the random thermal motion of air molecules. So your voice travels further in cold air than it does in warm air.

If the disturbance was continuous - such as a wave machine repeatedly moving up and down in the water for a long time - then the ripples which move outward would remain visible for as long as the disturbance lasts. New waves are being generated at the centre as fast as old waves are disappearing at the edge of the circle.

Generally, we study waves in an ideal situation that consists of no dissipative forces. In such an ideal situation, any mechanical wave would indeed travel forever to infinity in one direction if the medium extends to infinity because there is nothing to stop it (meaning nothing causes the wave to lose energy).

However, in reality various dissipative forces act on the mechanical waves (both transverse and longitudinal waves). These forces cause the waves to lose energy over time.

You can practically observe this in water waves. Some of its energy is converted to sound energy (energy of sound waves produced in medium surrounding water) which you can hear.

Also, when we study various waves in gaseous medium, we assume the medium to be an ideal gas for simplicity. Such a gas has no intermolecular forces. But real gases in the real world have intermolecular forces which resist the vibration of particles.

Another dissipative interaction is the absorption of energy by particles of medium. As waves travels through medium particles attain some energy. These particles may (they kind of always do) absorb some energy as thermal energy and pass the remaining energy to the next particle.

So, all these effects combine together to gradually cause the wave to lose energy to the extent that we are not able to detect it and finally, it ceases to even exist.

As mentioned by @OfekGillon and @Pieter, what I have described is generally termed as damping. However, there are some other important causes of what you have asked, attenuation being one of them.

According to Wikibooks, attenuation refers to combined effect of scattering and absorption which also cause the mechanical waves to lose energy.

NOTE: Waves disappear when particles of the medium stop vibrating, i.e. stop transfer of energy through medium. The effect of this decrease in vibration can be seen in decrease of amplitude. Intensity is proportional to square of amplitude. It is the energy transmitted per unit area per unit time. So, decrease in amplitude, energy or intensity refers to disappearing of a wave.

I hope this clears any doubts in your mind.

• don't forget the distribution of energy in all direction which attenuates the amplitude of the wave from the source as $\frac{1}{\sqrt{r^{d-1}}}$ (where $d$ is the dimension of the problem) Feb 12, 2020 at 15:36
• I agree that what @OfekGillon says is more important than damping. There is also the effect of dispersion. In a channel there can be solitons, no dispersion, only 1 dimension, and the amplitude does not go down much.
– user137289
Feb 12, 2020 at 16:44

As I understand, waves (the mechanical ones) are nothing but transfer of DISTURBANCE of the CONSTITUENT PARTICLES of a MEDIUM. But the constituents of a medium are not free from each other, implying that they are held together by some or the other cohesive forces.

Now as the particles at a given point in the medium are disturbed, they experience a restoring pull by the surrounding, hitherto undisturbed particles. We can call it shearing strain. In the process some energy is lost in the form of heat. With incremental loss of energy at every successive point along the course of propagation of a wave, the amplitude of the wave gradually decreases, ultimately to such a low value that it can't be identified from the "normal" disturbances of the constituent particles, which either may be inherent to the particles or are caused by other forces.

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Feb 26, 2023 at 10:44